Electricity Unit Summary

Electricity

The fundamental parts of electricity are charges.

Electrons usually carry a negative charge and protons carry a positive charge. Being that things are made out of protons and electrons, things are charged. If something has the same number of electrons as you do protons (same number of positive and negative charges) then it is neutral.



When an object is polarized, it means that one side of the charges have moved to one side of the object. That is, all the positive charges would have moved to one side, and the negative to the other so that one side of the object is positive and the other is negative, but the object is still neutral.

One kind of charged electricity we talked about was Static Electricity. 
There are three ways to charge something:

1.) Through Friction (by rubbing two things together)
2.) By Polarization. The way this works is that you bring an object over that is of either - or + charge and it attracts the opposite charge and repels the like charge. An example of this is when a balloon sticks to a wall. First you charge the balloon (-) using the aforementioned friction, then when you put it on the wall, the + attract and because the distance is less that the distance of the - charges repelling, the force is greater and the balloon sticks.
3.) Through Induction. Induction is similar to polarization in that you basically use a charged rod in the way of the balloon to polarize and object and then separate the two sides and you have two charged objects.

This image helps visualize it a little:

I mentioned before that a balloon sticks to a wall because of the distance between charges. This is because of Coulomb's Law which is....

F=kq1q2/d^2

Here the k is just a constant, and the two q's stand for charges. The force and distance are inversely (square) proportionate, so when the distance is lesser the force is greater and vise versa.

The Force that is push and pull of charges is caused by Electric Fields. - which is the area of influence (push or pull) around a charge. Basically, the energy is stored in the electric fields. 

The way you draw the electric field of a charge is by drawing arrows out from it indicating which way a positive charge would go. here is an example:

Electric Fields facilitate Electric Shielding. This is the reason we have metal casings around electronics, it protects the charges from being influenced by outside charges in the world. It works because the metal shield pulls the charges inside all around, and the pulls from one side cancel the pulls from the other, and the charge inside feels no force.

We did a podcast on Electric fields, here it is:



So, the Electric Fields hold the energy of the charge, the potential of this is called Electric Potential, which is the potential energy per charge. We call this Electric Potential Volts. 

We represent that as this formula:            V=PE (potential energy)/ q (charge)

When we have a difference in Volts, it is called Voltage. Sometimes we have something with high volts and something with low volts and the energy wants to travel from the High voltage to the Low.
This flow from high to low completes a circuit, and when the circuit is complete, then the energy is compelled to run through.

This flow of energy is called Current (represented with an I).
Ohm's Law defines the relationship between Current and Voltage:

I=V/R

The I is current and the V is change in Volts, but the R stands for Resistance. which are measured in ohms (the symbol for this is an omega sign in greek).
Resistance is something that is put in circuits to regulate the current despite what the voltage is.
Every normal outlet has a voltage of 120V, but appliances change their receptive currents for whatever the appliances needs are by adding resistors.

When you look at the equation, you can tell that the resistance and current can change but keep the voltage the same. The same is true for current. You can keep current the same, but still make an appliance more or less dangerous by increasing the resistance. for instance 5/10 and 2/4 are both equal to .5 (that would be the unchanged current), but the volts are 5V in one and 2V  in another by increasing the resistance.

The first box on this website explains resistance well and you can enter numbers to play around with how they all relate.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmlaw.html

There are two types of current: AC and DC
AC is alternating current, that is when the electrons move side to side as energy
DC is direct current, which is when they move forward.

There are a couple of things that affect current like
a.) thickness of what is traveling through. Thicker=more conducive
b.) Temperature- cold is better
c.) length- a short wire/tube is better

When we talk about actual circuits in places, often the circuits are parallel. What this means is that there are several appliances hooked up to a voltage source, and while they are hooked to the same source, they can operate autonomously. The alternative to this is a series circuit, which is set up to where each thing hooked up gets its current through the previous thing so, if one goes out they all do. Think christmas lights.

This is a great picture of what that looks like:

A parallel is preferable because you can turn one thing on without having to turn everything on. But, because on a series, everything is connected to the same line going to the source, when you add something, the current goes down because they are sharing and the resistance goes up. But in parallel, when you add one, you must increase the current to accomodate. 

To make sure that the current does't get too high and cause a fire or something horrible like that, we have fuses and circuit breakers. These will detect that the current is too high and break the circuit so that it isn't complete and the current won't flow 

A fuse is the same as a circuit breaker in purpose, but simply a different mechanism. 

to figure out the power you are using, you use the formula:

P=I/V which is measured in kw(kilowatts)/hr. 

To figure out how much it costs all together, you do this:

Power x hrs x $ per hour

And that's what we learned about Electricity!

Mousetrap Car Reflection

For the last few days, we have been working on making a car using a mousetrap to propel it. Our goal has been to make a car that goes five meters, and preferably with speed.
Yesterday we raced our cars, and here were the results:


Our car went an average velocity of .60 m/s.
(velocity = distance/time)
Distance: 5m
Time: 8.2 seconds
We came in last for our class as far as I know.

Here is a picture of the car we made:

and here is a diagram of it to make the individual parts clearer to see for reference when reading the following reflection.

Here is a video of our trial of our car going:


Reflection:

a.) Newton's First Law sates that an object in motion stays in motion unless acted upon by an outside force. In this case, the outside force is primarily Friction. The friction is needed to get the car going, you must utilize it to get it from going to not moving to moving. But you don't want so much that it also makes it go from moving to not moving.

Newton's Second Law states that Acceleration = Force/Mass. For this, you need a large Force which is the spring to provide the force to cause acceleration. Too large of a mass, however, would lower the acceleration, but you must consider that the mass contributes to friction, so you do need some.

Newton's Third Law states that every action has an equal and opposite reaction. In this case, the most relevant action/reaction pair is Wheel pushes on ground, ground pushes on wheel (you can see this drawn on the diagram above in green). The Force that is a part of the work that the wheel does when pushing on the ground is the Force causing acceleration. As we know from the previous two laws, that Force is important to how quickly the car accelerate, and also the friction of that action is important in starting the car quickly as well.

b.) The main part of the car that relied on Friction was the wheels, specifically the part that made contact with the ground. This friction was the Force that acted on the car so that it could go from not moving to moving. the more friction there was there, the easier it was for it to go from not moving to moving. For this friction, we wanted it to be more than just the edge of the CD because that did't have much friction. We instead put some electric tape in the edges so that it would have more friction. We didn't want to have too much friction there either or else it would slow down the car as well (be the force that made it go from moving to not moving quickly as the car lost speed). We thought the electric tape would be a good balance. Another part of the car that valued friction was the place where the string coiled around the axel. the more friction this part had, the faster the string would spin the axel as it unraveled. We did not have the time or wherewithal to tinker with this part, but I imagine it may have made our car go faster.

c.) We decided to choose a medium sized wheel in our CDs. We did not think this through particularly well, however, we figured that moderate was the best way to go for this project. It turns out we were right to assume because Bigger wheels actually crate a bigger lever arm which means there is more torque. However, it cannot just be as big as possible because the bigger it is the more rotational inertia it has which will make it more reluctant to rotate. So a medium size like CDs accommodates both the hinderance and the advantage of wheel size.

d.) The Energy of the car is put in as we pull the lever arm/ set the mousetrap, and it is stored in the spring until you release it. The energy stored in the spring is Potential Energy. Once you let the spring spring back, the Potential Energy turns into Kinetic Energy. This Energy is conserved as it converts. For instance, if we knew we stored 100J of Potential Energy in the spring when we pulled it back, then at the end of its route, the lever arm then has 100J of Kinetic Energy. In our car, we had a wooden lever arm that was attached to the mousetrap, when we pulled it back, we coiled the string attached to it around the axel in the back. When we released the lever arm, the potential energy converted to Kinetic Energy as it swung back towards the front and spun the wheel as it gathered kinetic energy.

e.) We First Knew that we didn't want the wheels to be too heavy because having more mass would mean there would be more rotational inertia. This would make the wheels reluctant to rotate, and thus reluctant to move. We also wanted to make the torque of the wheel (the radius) fairly big to make the rotational inertia lower. When we make the lever arm bigger, we would make the force needed smaller. But because we didn't want it too big because of the aforementioned inertia problem. SO we got a medium size wheel. Theoretically, the wheel is going to be spun the same amount of times every time we pull the spring back and let it loose. So when we have a larger wheel, it will cover more distance in the same rotation which is another reason to make the wheel a little bigger.

f.) We cannot calculate work that the spring does on the car because the work it does is not parallel but rather perpendicular to the distance the car goes. The force it does goes towards the ground, and the distance the car travels is forwards. In the same vain, The potential Energy that gets stored in the spring when we pull back gets converted into kinetic energy, but that energy does not go into propelling the car forward because the Force that is in the Kinetic Energy is not parallel to the distance either. We can't calculate the force that accelerate's the car because the Force that accelerates the car is not related to the other equations we do have the information for. So we cannot put the thing we do know about how it went forward, the distance, and find the force because we cannot use the work or KE equation as they are not parallel.

Reflection: 

a.)   Our initial design was fairly similar to our final design. We had to change many things, such as the lever arm and the string, but they were not drastic design changes we just had to make them better. If we could do the project again, the design would change, but I think we mostly adapted our design in the interest of time. We did look at other people's cars and add tape to the edges of the wheels for friction and we also stabilized our wheels fixed to the axels instead of loose around them by the suggestion of Veronica and Alex.

b.) One of the major problems was that it simply did not go far enough. The spring did not pull our axis like we thought it would when we first tested the car. We first realized that we hadn't put both of the little activators that stuck out from the spring on top of the lever arm. So when we did that we basically doubled the PE. That really helped. Then we also shortened the string and lever arm and finally got it to go further. Also our body was very flimsy as we tinkered with it it would bend on accident so we had to tape a wooden stick to it on the bottom and top so that it would be more stable and we wouldn't lose the energy in the spring going into bending the base.

c.) I would make the car longer and thinner and out of sturdier material. I would take more care with the axel wheel relationship because ours was sloppier than I would have liked and I think we lost a lot of energy there. Also make better use of the leveler because ours seemed wobbly. I think I would also try to only put friction on the pack wheels which are attached to the string.

d.) I might take more care with the preliminary steps to ensure that I was less likely to have to repeat certain parts because they were not done well the first time. In that same thought, I should worry much less about time and not feel rushed. Haste makes waste. Also some thought into which design to choose would be helpful because we sort of chose the first one that looked good. And also get materials in on time.

Work Unit Summary

This Unit we studied Work and some other concepts pertaining to it.
First we learned...

Work and Power:

Work = Force x Distance 
Work is measured in joules

The force and distanced used to calculate the work you do on something must be parallel. For instance is a box weighs a certain number of Newtons(upwards), and you take it across the room(forward), then you don't do work on the box.

Work is fairly similar to what you may think it is. The only misleading thing about our idea of work is that sometimes we may feel as though we are putting more or less work in when the work is actually the same.

One way it is misleading is that you may get tired doing work faster and thus think you have done more work. This isn't more work, it is more power.

Power is the time in which you do work. Power is measured in watts.
(Power = Work / time)

So, if you do something faster an end up feeling more tired, you just used more power, your work probably didn't change.

Note: 746 watts = one horsepower.

We then learned that Work is also related to Kinetic Energy:

Kinetic Energy is basically energy that a moving object has. 
the formula is: 

KE = (1/2)m(v)^2

So, you can calculate the KE for anything that you know has mass and velocity. (an object that is not moving does not have KE. Neither does an object with no mass.)

What we learned is that the change in KE is equal to Work
change in KE = Work

Often, we will calculate the change in KE in an object that speeds up or slows down over a distance(the velocity changes). We can jump between Work and KE(and then power if we know the time) by subtracting the final KE from the initial KE and then finding the Force by plugging it into Work = Force x Distance using the distance it changed KE.

Once we learned about Kinetic Energy, we learned about Conservation of Energy:

We learned that, when an object moves(or doesn't), it does not lose energy. The energy may be lost to heat or sound or light, however it is all accounted for. You also do not add Energy. 

An example is when an object is swinging on a string. When it is at the top of it's path(and it may be a t rest), it has a lot of Potential Energy but no Kinetic Energy. When it swings down, it starts to lose potential energy and gain Kinetic Energy until at the nadir of the path, it has a lot of Kinetic Energy and no Potential Energy. This relationship, in fact, is equal and opposite. 

change in KE = change in PE

You could relate this to the law of conservation of momentum because in a given situation(like an airbag in a car), you could use the fact that the change in momentum/energy is always the same to determine the factors that increase or decrease your injury in a car crash. 

With these added equations, we add on to the amount of steps we could use to go from, say, PE to Work. We could use PE = KE, and then use KE = Work to find, say, distance or force. 

To Apply these to actual actions, we talked about Machines: 
Specifically, simple machines.

Three types of simple machines are:
a ramp, a pulley, and a jack(for a car).


The way Machines work is they increase the distance over which the work is done so that the force is decreased and it feels easier. This is a way in which what we are doing can feel deceiving because we may be tempted to say that the work decreases because it feels easier. However, it is rather the case that

Work in = Work out
F(D) = F(D)

For instance, a ramp with increase the distance of the work you put in which makes the force you put in less. However, it still equals the same work out regardless.

We did a podcast on Machines which includes some helpful examples about how machines work and how efficient they are. Watch below to learn more.



Thanks for reading!

Unit 4 Summary

This Unit we learned about rotation.

Rotational and Tangential Velocity:

When speaking about rotation, there are two different kinds of velocity. There is rotational(or angular) velocity, and tangential(or linear) velocity.

Rotational velocity: measures how many times something rotates in a given unit of time. 

Tangential velocity: measures distance over in a given unit of time. This is the kind of velocity we were already familiar with. 

There are many situations where these two seem similar but are different. For instance when two children are riding on a merry go round, one on the outermost horse, and one on the inner most horse, their rotational speed is the same. If you can imagine, they rotate the same number of times per minute. However, the outermost child must cover more distance and therefore has a higher tangential velocity. 

Rotational Inertia:

Regular Inertia represents something's resistance to change.

Rotational Inertia: Rotational Inertia is specifically an objects resistance to change rotation. 

Inertia in regular circumstances is usually represented as mass. With rotational inertia it refers specifically to the distribution of the mass. When the mass is distributed further from the axis of symmetry, the rotational inertia increases. Be careful to not mistake this for increased rotational velocity. Inertia is resistance, so when the inertia increases, the rotational velocity decreases. The converse is true for when the inertia decreases. 

An Example of this is when an ice skater spins. When the ice skate pulls their arms(mass) in closer to their axis of symmetry, their rotational velocity increases. And when they extend their arms, they slow down. 

Conservation of Angular Momentum: 

We know very well that momentum is conserved. That is total momentum before = total momentum after.
The switch to angular momentum is ridiculously simple: angular momentum before = angular momentum after. 

And Rotational Momentum is also similar to normal momentum: 

Angular Momentum = (Rotational velocity x (Rotational Inertia)

This principle of conservation simply states that, for example the ice skater, would have the same angular momentum when she pulled her arms in as when she extended them out. This is because of the way inertia and velocity act opposite to each other. When inertia increases, velocity decreases and vise versa. They are always balancing each other out. 

Torque:

Torque is the thing that causes the rotation.

Torque is made up of two components: Force and Lever arm. 
Torque = Force x Lever Arm 

For instance in this picture, the side of the see saw with the girl on it has a greater Torque because she has a greater force, so it rotates with a counterclockwise torque.

Each rotation has a clockwise torque and a counterclockwise torque. 

When something is balanced, the two torques are equal. That is, 

Clockwise Torque = Counter Clockwise Torque

Here is an example of a meter stick that has been balanced on the edge of a table with a 100 gram weight on one side and the calculations to prove it is balanced:

*Remember that the Force is the Center of Gravity. The Lever Arm is the distance from the Center of Gravity to the axis of rotation. 

Center of Mass/Gravity:

To keep balanced you must keep your Center of Gravity over your base of support.

For instance, The leaning tower of Pisa is tilted, however, it's Center of Gravity is still over it's base of support.

This is why football players keep their feet further apart, because widening your base of support makes it easier to keep your Center of Gravity over it. And they are less likely to fall over. 

When wrestlers bend their knees, they do so to lower their center of gravity closer so that is, again, harder to get it out of the base of support, and thus harder to knock them over. 

Centripetal Force: 

Centripetal Force is a force that goes inwards from an object to the center as it rotates. 

This is why it is also called a center seeking force. 

It is a combination of an object that is already moving forward and the force of gravity downwards. 

Here is a picture of centripetal force:

(ps. sorry this is the lamest diagram ever...but it was either super simple or super complicated. If you need visual help check out the podcasts.)

Remember that centrifugal force is not real!

And that was Unit 4! 

Mass of the Meter Stick Lab

In this Lab, we were tasked in finding the mass of a given meter stick by using our knowledge of balance and torques. We were told to use a meter stick and a lead weight that weighs 100g. Once we had done our calculations, we would check the mass we got by actually weighing the meter stick and comparing the numbers. So we began....

Step 1:
First we did some demonstrations in order to better our understanding of torques, and to bestow on us the tools we need to find this information(the mass of the meter stick).

Here are the demos we did:

These exercises really helped us figure out the information we needed to gather and compile. We began to learn how to use the information we had to find more information.

Step 2: 

We began to plan after doing these demos. The demos were written in to solidify our ideas about balancing, but the planning was all vocal. We started to set it up and talk through way we might be able to calculate the mass.

Step 3:

Steps 2 and 3 bled together because trying out ways to find the mass were simultaneously our plans for doing them. The planning and the doing were not separate but we did them at the same time.

What we tried was a lot of writing numbers down and figuring out how they fit together. This is what finally worked:

We started by finding the Center of Gravity for the stick without the weight on it by balancing it on the edge of the table. It didn't end up being 50cm, it ended up being 50.3 cm. Then we added the weight to the end and tried to find the Center of Gravity again. That number we found was 28.7 cm.

Then we had to figure out what to do with those numbers. We knew that the meter stick was balancing, and when things are balanced, it is because their clockwise torque and counterclockwise torques are equal. We set up the equation that we set up in the demos to use the lever arms and force on one side to find the force on the other side.

clockwise torque=counterclockwise torque
Force * Lever Arm = Force * Lever Arm

Then we plugged in using .98 N instead of 100g for the weight because it needs to be in Newtons to be a force. We knew that 50.3 cm was still the center of gravity, so we subtracted 28.7 from 50.3 to find the lever arm of the side of the stick resting on the table. We got 21.6 cm, and used it as the lever arm for that side of the equation.

(.98) * (28.7) = (F) * (21.6) 

We found that the force on the right side(aka the entire meter stick, because we used that Center of Gravity) was 1.3 Newtons.
We converted that into mass using the w=mg equation because what we found with the torque equation was the weight of the meter stick. We use that equation to convert it to mass, which is what we are looking for and what we will measure. We found that the mass was 130g.

When we weighed it it was actually 120g. So we were off by ten grams which is kind of a bummer and void of satisfaction. Oh well, we learned about Physics anyway.

Here is a picture of our field notes:

Here is a Drawing of what is going on:

Resource Blog

Torque resource:

This resource is a Khan Academy tutorial/introduction to Torque. I found this video surprisingly informative because I had only seen a couple of science Kahn Academy videos but did not find them incredibly helpful. The ability to draw and animate movement by use of the medium he uses helps the effectiveness of teaching. It does teach the information a little bit differently from the video Ms. Lawrence made which is similar in style which may be confusing, however, it may also be very helpful. I found it helpful.

Link:

Introduction to torque: An introduction to torque


Center of Mass/Gravity resource: 

This page is a blog post on a blog I hadn't heard of but is apparently made by or funded by PBS. This source integrates torque in as well which helps to relate them. The flow of the post is intuitive and east to follow, and it begins with an example to strengthen understanding through real-life. Over all I found this source very helpful.

Link:

http://www.pbs.org/opb/circus/classroom/circus-physics/center-mass/

Unit 3 Summary

1.) Newton's Third Law and Action Reaction Pairs:

 Newton's Third Law: Every action has an equal and opposite reaction.

For instance, a pair of tug of war teams are always pulling on each other with equal and opposite forces. A car and a truck crashing exert equal and opposite forces on each other. You state this pair like this:

Car pushes truck forward
Turck pushes car backward
(be sure to include vectors)

Or a skateboard:

- The effect that makes a difference in the pairs, especially one like the tug of war example, is friction. The greater force of friction allows one team or the other to win. Two things that affect friction are weight and the nature of the surface.

- Many times there are multiple action reaction pairs for every situation. For example, a grapefruit sitting on a table is pairing with both the earth and the table. These pairs are not equal and opposite necessarily, only the individual pairs are equal and opposite.
- Make sure to remember that accelerations in the opposite direction are negative.

This page contains great practice questions for understanding Newton's Third Law.

2.) Vectors 

Vectors are a device that show both direction and magnitude.  
More simply, vectors are arrows. We show magnitude with the length (and possibly opaqueness if you want) of the arrow, and the direction is the direction the arrow is pointing.

Adding vectors is helpful when determining the actual direction something will be traveling and the speed at which it will be traveling, by considering the forces acting upon the object.


A good example is a canoe on a river. If there is a current running south and you are paddling east, using vectors, you can determine where the canoe's path will take.

To add these vectors, draw lines parallel to each of the existing vectors, and then the line of actual direction is from the center to the intersection of the parallels.
Use this method also to help determine tension.

When trying to determine a lesser or greater tension, inverse the parallels so that they intersect the opposite line. The tension is represented by the distance between the center and the points of intersection. Be sure to put direction on the friction lines- I have made this mistake before. 

3.) Tides/Gravitational Force  
The formula for Gravitational Force is F=G m1m2/d^2

This formula explains the gravitational force between masses like planets. 
This equation and the information we can extract from it help explain a lot of things including tides.

Tides are caused by the gravitational force between the moon and the earth. Even though the sun has much (much much much) more mass, the closeness of the moon ultimately makes the force between the moon and earth greater and have a greater effect. 

The equation dictates that distance between the objects and the force are inversely proportionate. Same with mass, so the close distance between the moon and Earth made up for it's small mass.


-The Earth has a tidal bulge around it that is created by the moon's gravitational force and it creates high tides on each side of the moon and low tides on the adjacent sides.  The tides are caused by a difference in force from the moon because the distance is different at the two points relative to the center of the moon. There are six hours between each low and high tide and 12 between high tides and 12 between low tides. So, there are two low tides and two high tides each day. 

- When the moon and sun and earth are in line, the tides are called spring tides which are higher than the normal high, and lower than the normal low.When the sun is not in line it is rather during a quarter phase of orbit, it is called a neap tide. These tides are more lukewarm than the spring tides, in fact they are lower than the normal time tides. 

                                                           

This video is really helpful in understanding tides:

3.) Momentum and the Conservation of it

The momentum formula is p=mv
(the units for p is therefore kgm/s)

p total before= p total after (because of Newton's Third Law)



An important detail about momentum is that the momentum os a system is conserved. That is, 

When we are assessing two objects, like carts, collide, we can calculate the speed after by taking this assumption. Use this equation:

MaVa+MbVb= (Vab)(Ma+b)    - plug in the masses and velocities to find the velocity after the carts collide.

 
3b.) Impulse
Impulse (or J) is the change in momentum.

To change momentum, you need a change in force.
When thinking about changing the Force, two main things matter: 

1. The amount of Force applied  2. Time F is applied

For these things, we explain the equation for Impulse: J=F(change in t)

This equation shows that distance and force react in a certain way to each other. When time increases force decreases and vise versa. 

An Example of this would be landing on a hardwood floor rather than a memory foam mattress. The mattress increases the time of force applied (do not forget that the change in momentum/impulse is the same), which decreases the force. That is why you wouldn't get as hurt on the mattress. 
When answering these problems be sure to mention:

-That the object will go from moving to not moving no matter what
- The relationship between change in momentum and impulse
- The relationship between time and force when talking about impulse

This page helps to connect Newton's Second Law, Newton's Third Law and Change in Momentum in contribution to Impulse. The building blocks are really good to understand so check it out.